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CS 115: COMPUTING FOR The Socio-Techno Web

CS 115: COMPUTING FOR The Socio-Techno Web. The fun and the fear of Online Social Networks. What is an online social network?. A set of relationships between entities. Relationships (Networks) and Graphs. friend. Movie 1. co-worker. Mary. Actor 2. Peter. Actor 1. Actor 4. Albert.

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CS 115: COMPUTING FOR The Socio-Techno Web

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  1. CS 115: COMPUTING FOR The Socio-Techno Web The fun and the fear of Online Social Networks

  2. What is an online social network? A set of relationships between entities

  3. Relationships (Networks) and Graphs friend Movie 1 co-worker Mary Actor 2 Peter Actor 1 Actor 4 Albert Movie 3 friend brothers Movie 2 Albert Actor 3 Protein 2 Protein 1 Protein 5 Protein 9 N=4 L=4 Network Science: Graph Theory 2012

  4. online social Network (fb)

  5. A powerful network

  6. Representing a Social Network 8 3 a set V of n nodes or vertices, usually denoted {v1, …, vn} node v2 a set E of m edges between nodes, usually denoted {ei,j} un-directed or directed (arcs) uni-directed of bi-directed edge e8,3

  7. 1 2 8 3 7 4 5 6 Paths Path (v1,v2,v8,v3,v7) Definition: A path is a sequence of nodes (v1, …, vk) such that for any adjacent pair vi and vi+1, there’s an edge ei,i+1 between them.

  8. Paths “I date(d) someone who date(d) someone who date(d) you.”

  9. Examples of Social Networks What do you observe?

  10. 1 2 8 3 7 4 5 6 Path length Path (v1,v2,v8,v3,v7) has length 4. Definition: The length of a path is the number of edges it contains.

  11. Connected GRAPH • A graph is connected when there is a path between every pair of vertices. In a connected graph, there are no unreachable vertices. • a connected component of an undirected graph is a subgraph in which any two vertices are connected to each other by paths, and which is connected to no additional vertices in the super graph.

  12. 1 2 8 3 7 4 5 6 Distance The distance between v1 and v7 is 3. Definition: The distance between nodes vi and vj is the length of the shortest path connecting them.

  13. Famous distances nodes = {actors} edges = if two actors star in same film Kevin Bacon number Kevin Bacon number = distance between actor and Bacon

  14. Title Data

  15. Famous distances Math PhD genealogies

  16. ErdősNumbers Erdős wrote 1500+ papers with 507 co-authors. Number of links required to connect scholars to Erdős, via co-authorship of papers What type of graph do you expect? Jerry Grossman (Oakland Univ.) website allows mathematicians to compute their Erdős numbers:http://www.oakland.edu/enp/ Connecting path lengths, among mathematicians only: • avg = 4.65 • max = 13

  17. Famous distances nodes = {mathematicians} edges = if 2 mathematicians co-author a paper Paul Erdősnumber Erdős number = distance between mathematican and Erdos

  18. Proud people!

  19. Famous distances Erdős number of … = 4

  20. Famous distances Erdős number of … = 3 Erdos Fan Chung F.T. Leighton P.T. Metaxas

  21. Famous distances Erdősnumber of … = 4 Orit Shaer Erdos Fan Chung P.T. Metaxas F.T. Leighton

  22. Famous distances Erdos number of … if you publish with Takis! YOU = Bill Gates

  23. 1 2 8 3 7 4 5 6 Diameter The diameter is 3. Definition: The diameter of a graph is the maximum shortest-path distance between any two nodes.

  24. The diameter of a social network is small. Milgram’s experiment (1960s). Ask someone to pass a letter to another person via friends knowing only the name, address, and occupation of the target.

  25. Small world phenomenon Bernard, David’s cousin who went to college with David, mayor of Bob’s town Bob, a farmer in Nebraska Maya, who grew up in Boston With Lashawn

  26. Milgram: Six Degrees of Separation • 296 People in Omaha, NE, were given a letter,asked to try to reach a stockbroker in Sharon, MA,via personal acquaintances • 20% reached target • average number of “hops” in the completed chains = 6.5 • Why are chains so short? • I know!Exponential growth of friends!

  27. Today we can measure this with 2 billion people • The majority of Facebook users (~2 billion people) have an average between 3 and 4 steps.

  28. Why are Chains so Short? If I count my friends’ friends’ friends… 1 2 22 + 2d 2d+1 - 1  diameter = log n

  29. Birds of a feather flock together... Homophily • Adamic, L. A., & Glance, N. (2005, August). The political blogosphere and the 2004 US election: divided they blog. In Proceedings of the 3rd international workshop on Link discovery (pp. 36-43). ACM.

  30. Polarity

  31. Huge Echo Chamber

  32. Social Algorithms

  33. Filter Bubble

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